The invention refers to those systems or apparatus that sealingly weld a closing film on at least one tray containing a product to be packaged. The apparatus according to the invention is of the type with facing bell members, classifiable in IPC B65B31/04, capable of producing packages of the kind known as MAP (Modified Atmosphere Packages), in which the product is enclosed inside a sealed package containing a modified atmosphere useful to improve the preservation of the product, without any substantial difference in pressure between inside and outside. In order to modify the atmosphere inside the pack, in a step in which the barrier film is placed over the product placed in the tray for subsequent closing, kept at a suitable distance from the perimeter edge of the same tray, the air is firstly removed from the inside of the tray and then replaced with a modified atmosphere, for example based on nitrogen, carbon dioxide, oxygen and/or other gases. The prior art closest to the invention is described in the Italian patent application No. BO2011A-000403 dated Jul. 6, 2011, in the name of the same Applicant, which refers to an apparatus comprising a top bell member which is open downwards, usually containing the welding means and also the means for cutting the barrier film for closing the trays and comprising a bottom bell member, facing the preceding bell member and open in this direction, with a chamber and with a seat for housing at least one tray which may be inserted into and extracted from the said seat by specific means, comprising means for cyclic positioning of an extended portion of film between the said two open bell members and above the trays placed in the bottom bell member, which also comprises means for moving the said bell members towards each other, to close between them the edge of the tray and over this said film and comprising means for performing in this sequence the steps of extraction of the air from the tray and introduction of process gases therein for preservation of the produced place in the tray before to the subsequent step of welding of the film on the edge of the same tray and cutting of the perimeter of the portion of film welded to the same tray. This apparatus comprises means for ensuring that during the step for mutual closing of the bell members, these form therein a main chamber defined at the top by the film for covering the tray, at the bottom by the same tray with the product and at the side by any interface structure that surrounds and connects the perimeter of the said film to the perimeter of the top edge of the tray and on the structure of which holes or slots are provided, suitably distributed and positioned on the outside of the perimeter of the tray and communicating with the said main chamber. In the same apparatus according to the prior art indicated above, when the two bell members are closed, two volumes, which do not directly communicate which each other, are formed inside the said bell members, a first volume formed by the said main chamber, with the tray and with the covering film, and a second volume formed by the internal intercommunicating chambers of the said two bell members. Some of the holes of the said interface structure open out substantially along a portion or side of the tray and are connected to a first header or circuit located in the bottom bell member, while other said holes open out along at least one portion or opposite side of the same tray and are connected to a second header or circuit also located inside the bottom bell member, whereas the internal chambers are connected to one another and to at least a third circuit, Means are provided such that, via the said first and second header or circuit, connected to the said main chamber and via the said third circuit connected to the internal chambers of the two bell members, it is possible to produce MAP-type packages without having to previously form very high vacuums in the trays and limiting the use of process gases. An apparatus of this type has a certain degree of structural complexity, must be reprogrammed to vary the format of the trays and also requires complex calibration to balance the two volumes concerned in the step of introducing the process gas and the balancing step, in order to obtain packages always with the desired appearance.